LCM of 312 and 357
37128 is the LCM of 312 and 357. The step-by-step solution using prime factors and special division methods is one of the simple methods to easily understand how to find what is the LCM of 312 and 357, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 312 and 357?
lcm (312 357) = (?)
312 => 2 x 2 x 2 x 3 x 13
357 => 3 x 7 x 17
= 3 x 2 x 2 x 2 x 13 x 7 x 17
= 37128
lcm (312 and 357) = 37128
37128 is the LCM of 312 and 357.
where,
312 is a positive integer,
357 is a positive integer,
37128 is the LCM of 312 and 357,
{3} in {2 x 2 x 2 x 3 x 13, 3 x 7 x 17} is the common factors of 312 and 357,
{2 x 2 x 2 x 13 x 7 x 17} in {2 x 2 x 2 x 3 x 13, 3 x 7 x 17} are the uncommon factors of 312 and 357.
Use in Mathematics: LCM of 312 and 357
The below are some of the mathematical applications where lcm of 312 and 357 can be used:
- to find the least number which is exactly divisible by 312 and 357.
- to find the common denominator for two fractions having 312 and 357 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 312 and 357 helps to find the exact time when two similar and recurring events with different time schedule happens together at the same time. For example, the real world problems involve lcm in situations to find at what time the bells A and B all toll together, if bell A tolls at 312 seconds and bell B tolls at 357 seconds repeatedly. The answer is that all bells A and B toll together at 37128 seconds for the first time, at 74256 seconds for the second time, at 111384 seconds for the third time and so on.
Important Notes: 312 and 357 lcm
The below are the important notes to be remembered while solving the lcm of 312 and 357:
- The common prime factors and the remaining prime factors of 312 and 357 should be multiplied to find the least common multiple of 312 and 357, when solving lcm by using prime factors method.
- The results of lcm of 312 and 357, and the lcm of 357 and 312 are identical, it means the order of given numbers in the lcm calculation doesn't affect the results.
How-to: What is the LCM of 312 and 357?
The below solved example with step by step work shows how to find what is the lcm of 312 and 357 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 312 and 357?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 312
B = 357
What to be found:
find the lcm of 312 and 357
step 2 Find the prime factors of 312 and 357:
Prime factors of 312 = 2 x 2 x 2 x 3 x 13
Prime factors of 357 = 3 x 7 x 17
step 3 Identify the repeated and non-repeated prime factors of 312 and 357:
{3} is the most repeated factor and {2 x 2 x 2 x 13 x 7 x 17} are the non-repeated factors of 312 and 357.
step 4 Find the product of repeated and non-repeated prime factors of 312 and 357:
= 3 x 2 x 2 x 2 x 13 x 7 x 17
= 37128
lcm(312 and 357) = 37128
Hence,
lcm of 312 and 357 is 37128
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 312 and 357.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 312 and 357
What to be found:
lcm (312, 357) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
312 and 357
step 3 Choose the divisor which divides each or most of the given integers (312 and 357), divide each integers separately and write down the quotient in the next line right under the respective integers. Bring down the integer to the next line if any integer in 312 and 357 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 312 | 357 |
| 2 | 156 | 357 |
| 2 | 78 | 357 |
| 3 | 39 | 357 |
| 7 | 13 | 119 |
| 13 | 13 | 17 |
| 17 | 1 | 17 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 312 and 357:
= 2 x 2 x 2 x 3 x 7 x 13 x 17
= 37128
LCM(312, 357) = 37128
The LCM of two numbers 312 and 357 is 37128